The bacteria in a Petri dish culture are self-duplicating at a rapid pace. The relationship between the elapsed time $t$, in minutes, and the number of bacteria, $B(t)$, in the Petri dish is modeled by the following function. B ( t ) = 10 ⋅ 2 t 12 B(t)=10 \cdot 2\^{\frac{t}{12}} How many bacteria will make up the culture after $120$ minutes? Round your answer, if necessary, to the nearest hundredth.
Solution: Thinking about the problem We want to find the number of bacteria in the culture after $120$ minutes. In other words, we are given a $t$ value of $120$ minutes and want to find the number of bacteria associated with that input, or $B(120)$. To do this, we can substitute ${120}$ in for $ t$ and evaluate. B ( 120 ) = 10 ⋅ 2 120 12 B( {120})=10 \cdot 2\^{\frac{{120}}{12}} Evaluating the expression We can use a calculator to evaluate the expression. The answer is shown below. B ( 120 ) = 10 ⋅ 2 120 12 = 10 ⋅ 2 10 = 10,240 \begin{aligned}B(120)&=10 \cdot 2\^{\frac{{120}}{12}}\\\\ &=10\cdot 2^{{10}}\\\\ &=10{,}240\\\\ \end{aligned} There will be $10{,}240$ bacteria in the culture after $120$ minutes.